Finite Group Databasebeta

← #29665515

Subgroups — #29665515

Order 15616.

608 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456966C211yesmaximal, characteristic, complemented
2#21455633C211yesmaximal, characteristic
3#21455602C211yesmaximal, characteristic
4#21454929C211yesmaximal, characteristic
5#21445275C211yesmaximal, characteristic, complemented
6#21445269C211yesmaximal, characteristic, complemented
7#21445267C211yesmaximal, characteristic, complemented
8#21445223C211yesmaximal, characteristic, complemented
9#21445221C211yesmaximal, characteristic, complemented
10#21445219C211yesmaximal, characteristic, complemented
11#21445217C211yesmaximal, characteristic, complemented
12#21444592C211yesmaximal, characteristic, complemented
13#21444508C211yesmaximal, characteristic, complemented
14#333×D61C211yesmaximal, characteristic, complemented
15C61×#1684C211yesmaximal, characteristic, complemented
16#16840317C2211yescharacteristic
17C4⋊Q8×D61C2211yescharacteristic
18C4×#11758226C2211yescharacteristic
19#16840167C2211yescharacteristic
20#16840165C2211yescharacteristic
21#16840112C2211yescharacteristic
22#16840096—21no—
23#16840096—21no—
24#16840067—21no—
25#16840061—21no—
26#16840057C2211yescharacteristic
27#16840057C2211yescharacteristic
28#16840055—21no—
29#16840055—21no—
30#16840053C2211yescharacteristic
31#16840053C2211yescharacteristic
32#16840049C2211yescharacteristic
33#16840045—21no—
34#16840041—21no—
35#16840039C2211yescharacteristic
36Q8×#92418C2211yescharacteristic
37C8×D244—21no—
38C8×D244C2211yescharacteristic
39#16839827—21no—
40#16839827C2211yescharacteristic
41#16839813—21no—
42#16839813C2211yescharacteristic
43#16839803—21no—
44#16839797—21no—
45#16839784C2211yescharacteristic
46C4⋊C8×D61—21no—
47C4⋊C8×D61C2211yescharacteristic
48C4⋊C8×D61C2211yescharacteristic
49#16839762—21no—
50#16839757—21no—
51#16839515C2211yescharacteristic
52#16839514C2211yescharacteristic
53#16839514C2211yescharacteristic
54#16839511C2211yescharacteristic
55#16839510C2211yescharacteristic
56#16839510C2211yescharacteristic
57#16839510C2211yescharacteristic
58#16839510C2211yescharacteristic
59#16839508C2211yescharacteristic
60C61×#487C2211yescharacteristic
61C61×#477C2211yescharacteristic
62C61×#475C2211yescharacteristic
63C8×Q8×C61C2211yescharacteristic
64C61×#335C2211yescharacteristic
65C61×#333C2211yescharacteristic
66C61×#332C2211yescharacteristic
67C2×#11758226D411yescharacteristic
68C2×Q8×D61—21no—
69C2×#11758189—21no—
70C2×C8×D61—21no—
71C2×C8×D61—21no—
72C2×C8×D61—21no—
73C2×C8×D61—21no—
74#14519777C2311yescharacteristic
75#14519777C2311yescharacteristic
76#14519776—21no—
77#14519776—21no—
78#14519775—21no—
79#14519768—21no—
80#14519757—21no—
81#14519753—21no—
82Q8×Dic61—21no—
83Q8×Dic61D411yescharacteristic
84#14519742—21no—
85C4×D244—21no—
86C4×D244C2311yescharacteristic
87#14519739—21no—
88#14519739D411yescharacteristic
89#14519735—21no—
90#14519735—21no—
91#14519735D411yescharacteristic
92C4⋊C4×D61—21no—
93C4⋊C4×D61—21no—
94C42×D61—21no—
95C42×D61C2311yescharacteristic
96#14519711—21no—
97#14519711—21no—
98#14519710—21no—
99#14519710—21no—
100#14519710—21no—
101#14519710—21no—
102#14519710—21no—
103#14519709—21no—
104#14519709—21no—
105#14519708—21no—
106C4⋊#92418—21no—
107C4⋊#92418C2311yescharacteristic
108C4⋊#92418C2311yescharacteristic
109C4⋊#92418C2311yescharacteristic
110#14519706—21no—
111#14519706—21no—
112#14519706—21no—
113#14519706D411yescharacteristic
114#14519706D411yescharacteristic
115#14519701—21no—
116#14519701—21no—
117#14519701—21no—
118#14519701—21no—
119#14519699—21no—
120#14519699—21no—
121#14519697—21no—
122#14519697—21no—
123#14519689—21no—
124#14519689—21no—
125#14519689D411yescharacteristic
126#14519689D411yescharacteristic
127C4×#92418—21no—
128C4×#92418C2311yescharacteristic
129C4⋊Q8×C61C2311yescharacteristic
130C4⋊Q8×C61C2311yescharacteristic
131C4×Q8×C61C2311yescharacteristic
132#107×C61—21no—
133#106×C61—21no—
134C4⋊C8×C61—21no—
135C4⋊C8×C61C2311yescharacteristic
136C4⋊C8×C61C2311yescharacteristic
137C4⋊C8×C61C2311yescharacteristic
138#103×C61—21no—
139#103×C61—21no—
140#103×C61—21no—
141#103×C61—21no—
142C4×C8×C61—21no—
143C4×C8×C61C2311yescharacteristic
144C2×Q8×C61—21no—
145C2×Q8×C61—21no—
146C2×Q8×C61C2×D411yescharacteristic
147#11758226—22no—
148#11758226Q1614yes—
149Q8×D61—82no—
150C2×D244—21no—
151C2×D244C2×D411yescharacteristic
152C2×C4×D61—21no—
153C2×C4×D61—21no—
154C2×C4×D61—21no—
155C2×C4×D61—41no—
156C2×C4×D61C2×D411yescharacteristic
157C2×C4×D61C2×D411yescharacteristic
158C2×C4×D61#4111yescharacteristic
159C2×Dic122—21no—
160C2×Dic122—21no—
161C2×Dic122—41no—
162C2×C8×C61—21no—
163C2×C8×C61—21no—
164C2×C8×C61—21no—
165C2×C8×C61C2×D411yescharacteristic
166C2×C8×C61C2×D411yescharacteristic
167C4⋊C4×C61—21no—
168C4⋊C4×C61—21no—
169C4⋊C4×C61—21no—
170C4⋊C4×C61—21no—
171C4⋊C4×C61—21no—
172C4⋊C4×C61C2×D411yescharacteristic
173C42×C61—21no—
174C42×C61C2411yescharacteristic
175#11758198—21no—
176#11758198—21no—
177#11758198—21no—
178#11758198—41no—
179C4⋊Dic61—21no—
180C4⋊Dic61—21no—
181C4⋊Dic61—21no—
182C4⋊Dic61—21no—
183C4⋊Dic61—21no—
184C4⋊Dic61—41no—
185C4⋊Dic61C2×D411yescharacteristic
186#11758196—41no—
187#11758196—41no—
188#11758196—41no—
189C4×Dic61—21no—
190C4×Dic61—21no—
191C4×Dic61—41no—
192C4×Dic61C2×D411yescharacteristic
193C4×Dic61C2×D411yescharacteristic
194C4×Dic61#4111yescharacteristic
195C2×#92418—21no—
196C2×#92418—21no—
197C2×#92418—21no—
198C2×#92418C2×D411yescharacteristic
199C2×#92418C2×D411yescharacteristic
200#11758189—42no—
201C8×D61—42no—
202C8×D61—81no—
203C8×D61—81no—
204C8×D61—81no—
205C22×D61—21no—
206C22×D61#12111yescharacteristic
207Q8×C61—21no—
208Q8×C61—41no—
209Q8×C61—41no—
210Q8×C61—81no—
211Q8×C61C2×Q1612yes—
212C2×C4×C61—21no—
213C2×C4×C61—21no—
214C2×C4×C61—41no—
215C2×C4×C61—41no—
216C2×C4×C61C22×D411yescharacteristic
217C2×C4×C61C22×D411yescharacteristic
218C2×C4×C61C2×#4111yescharacteristic
219C2×Dic61—21no—
220C2×Dic61—41no—
221C2×Dic61—41no—
222C2×Dic61#12111yescharacteristic
223C2×Dic61#12111yescharacteristic
224C2×Dic61#12111yescharacteristic
225D244—24no—
226D244—21no—
227D244C2×Q1612yes—
228C4×D61—21no—
229C4×D61—21no—
230C4×D61—24no—
231C4×D61—41no—
232C4×D61—41no—
233C4×D61—41no—
234C4×D61—81no—
235C4×D61—82no—
236C4×D61C2×Q1612yes—
237C4×D61#13512yes—
238Dic122—82no—
239Dic122—81no—
240Dic122—81no—
241C8×C61—21no—
242C8×C61—21no—
243C8×C61—41no—
244C8×C61—41no—
245C8×C61—41no—
246#92418—21no—
247#92418—21no—
248#92418—41no—
249#92418—41no—
250#92418—41no—
251#19417—611nomaximal, Sylow
252C22×C61C2×#12111yescharacteristic
253C2×D61—21no—
254C2×D61—21no—
255C2×D61—22no—
256C2×D61—41no—
257C2×D61—41no—
258C2×D61#46712yes—
259C4×C61—22no—
260C4×C61—21no—
261C4×C61—41no—
262C4×C61—81no—
263C4×C61—81no—
264C4×C61C22×Q1611yescharacteristic
265C4×C61C2×#13511yescharacteristic
266C4×C61#57711yescharacteristic
267C4×C61#57811yescharacteristic
268Dic61—21no—
269Dic61—21no—
270Dic61—41no—
271Dic61—81no—
272Dic61—81no—
273Dic61#46712yes—
274#3230—611no—
275#3079—611no—
276#3076—611no—
277#2988—611no—
278#1684—611no—
279#1684D6111yescharacteristic, complemented
280#1683—611no—
281#1683—611no—
282#1676—611no—
283#1676—611no—
284#1675—611no—
285#1675—611no—
286#1571—611no—
287#1550—611no—
288C2×#333—611no—
289C2×C61#304611yescharacteristic
290C2×C61C2×#46711yescharacteristic
291C2×C61#306811yescharacteristic
292D61—22no—
293D61—42no—
294#533—611no—
295C2×C4⋊Q8—611no—
296C4×#41—611no—
297#500—611no—
298#500—611no—
299#487—611no—
300#487C2×D6111yescharacteristic
301#484—1221no—
302#484—1221no—
303#479—1221no—
304#478—1221no—
305#477—611no—
306#477—611no—
307#477—1221no—
308#477—1221no—
309#477C2×D6111yescharacteristic
310#476—611no—
311#476—611no—
312#476—611no—
313#475—1221no—
314#475C2×D6111yescharacteristic
315#474—611no—
316#474—1221no—
317C8×Q8—611no—
318C8×Q8C2×D6111yescharacteristic
319C8×D4—611no—
320C8×D4—611no—
321C8×D4—1221no—
322C8×D4—1221no—
323#431—611no—
324#431—1221no—
325#428—1221no—
326#427—1221no—
327#423—611no—
328C2×C4⋊C8—611no—
329C2×C4⋊C8—611no—
330C2×C4⋊C8—1221no—
331#417—1221no—
332#416—1221no—
333#335—611no—
334#335—611no—
335#335—611no—
336#335C2×D6111yescharacteristic
337#333—611no—
338#333—611no—
339#333—611no—
340#333—611no—
341#333—611no—
342#333C2×D6111yescharacteristic
343#332—611no—
344#332C2×D6111yescharacteristic
345C61#1941711yescharacteristic, complemented, Sylow
346C2×#41—611no—
347C22×Q8—1221no—
348C2×M16—1221no—
349C22×C8—1221no—
350C22×C8—1221no—
351C22×C8—1221no—
352C22×C8—1221no—
353C4⋊Q8—611no—
354C4⋊Q8—611no—
355C4⋊Q8—1221no—
356C4⋊Q8—1221no—
357C4⋊Q8—1221no—
358C4⋊Q8C22×D6111yescharacteristic
359C4⋊Q8C22×D6111yescharacteristic
360#125—1221no—
361C22⋊Q8—1221no—
362C22⋊Q8—1221no—
363C4×Q8—611no—
364C4×Q8—1221no—
365C4×Q8—1221no—
366C4×Q8C22×D6111yescharacteristic
367C4×D4—611no—
368C4×D4—611no—
369C4×D4—1221no—
370C4×D4—1221no—
371#117—611no—
372#117—1221no—
373#117—1221no—
374C2×C4⋊C4—1221no—
375C2×C4⋊C4—1221no—
376C2×C42—611no—
377C2×C42—1221no—
378#107—21no—
379#107—1221no—
380#107—1221no—
381#107—1221no—
382#107—1221no—
383#107—1221no—
384#107—1221no—
385#107—1221no—
386#106—21no—
387#106—1221no—
388#106—1221no—
389#106—1221no—
390C4⋊C8—21no—
391C4⋊C8—611no—
392C4⋊C8—611no—
393C4⋊C8—611no—
394C4⋊C8—611no—
395C4⋊C8—611no—
396C4⋊C8—1221no—
397C4⋊C8—1221no—
398C4⋊C8—1221no—
399C4⋊C8—1221no—
400C4⋊C8C22×D6111yescharacteristic
401C4⋊C8C22×D6111yescharacteristic
402C4⋊C8C22×D6111yescharacteristic
403#103—21no—
404#103—21no—
405#103—21no—
406#103—21no—
407#103—1221no—
408#103—1221no—
409#103—1221no—
410#103—1221no—
411#102—1221no—
412#102—1221no—
413#102—1221no—
414#102—1221no—
415C22⋊C8—611no—
416C22⋊C8—611no—
417C22⋊C8—1221no—
418C22⋊C8—1221no—
419C4×C8—21no—
420C4×C8—611no—
421C4×C8—1221no—
422C4×C8C22×D6111yescharacteristic
423#41—614no—
424#41—1222no—
425C2×Q8—21no—
426C2×Q8—21no—
427C2×Q8—1221no—
428C2×Q8—1221no—
429C2×Q8—4882no—
430C2×Q8—2441no—
431C2×Q8D4×D6111yescharacteristic
432C2×D4—611no—
433C2×D4—1221no—
434C22×C4—611no—
435C22×C4—611no—
436C22×C4—611no—
437C22×C4—1221no—
438C22×C4—1221no—
439C22×C4—1221no—
440C22×C4—2441no—
441M16—2442no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—611no—
446C2×C8—611no—
447C2×C8—1221no—
448C2×C8—1221no—
449C2×C8—1221no—
450C2×C8—4881no—
451C2×C8—4881no—
452C2×C8—4881no—
453C2×C8—2442no—
454C2×C8D4×D6111yescharacteristic
455C2×C8D4×D6111yescharacteristic
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—611no—
462C4⋊C4—1221no—
463C4⋊C4—1221no—
464C4⋊C4—1221no—
465C4⋊C4—1221no—
466C4⋊C4—1221no—
467C4⋊C4—2441no—
468C4⋊C4—2441no—
469C4⋊C4—2441no—
470C4⋊C4—2441no—
471C4⋊C4D4×D6111yescharacteristic
472C22⋊C4—1221no—
473C22⋊C4—1221no—
474C22⋊C4—1221no—
475C22⋊C4—2441no—
476C42—21no—
477C42—611no—
478C42—611no—
479C42—611no—
480C42—1221no—
481C42—1221no—
482C42—2441no—
483C42C23×D6111yescharacteristic
484C23—611no—
485C23—1221no—
486Q8—21no—
487Q8—41no—
488Q8—41no—
489Q8—81no—
490Q8—4881no—
491Q8—4881no—
492Q8—4882no—
493Q8Q16×D6112yes—
494D4—612no—
495D4—1224no—
496D4—1221no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—611no—
502C2×C4—612no—
503C2×C4—612no—
504C2×C4—611no—
505C2×C4—611no—
506C2×C4—1224no—
507C2×C4—1221no—
508C2×C4—1221no—
509C2×C4—1221no—
510C2×C4—4881no—
511C2×C4—4882no—
512C2×C4—2441no—
513C2×C4—2441no—
514C2×C4—2441no—
515C2×C4—2441no—
516C2×C4—2441no—
517C2×C4C2×D4×D6111yescharacteristic
518C2×C4C2×D4×D6111yescharacteristic
519C2×C4#41×D6111yescharacteristic
520C8—21no—
521C8—21no—
522C8—41no—
523C8—41no—
524C8—41no—
525C8—1221no—
526C8—1221no—
527C8—2441no—
528C8—2441no—
529C8—2441no—
530C22—612no—
531C22—1221no—
532C22—1221no—
533C22—1222no—
534C22—2441no—
535C22—2441no—
536C22#121×D6111yescharacteristic
537C4—22no—
538C4—21no—
539C4—41no—
540C4—81no—
541C4—81no—
542C4—612no—
543C4—1221no—
544C4—1221no—
545C4—4881no—
546C4—4881no—
547C4—2441no—
548C4C2×Q16×D6111yescharacteristic
549C4#135×D6111yescharacteristic
550C4#1684056911yescharacteristic
551C4#1684057811yescharacteristic
552C2—1222no—
553C2—2442no—
554C2#2145537211yescharacteristic
555C2#467×D6111yescharacteristic
556C2#2145554211yescharacteristic
subgroupG/H
centerC22#121×D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#1684C2
socleC22×C61C2×#121
prime radicalC2×#11758226D4
hypercenter#1684D61
hypocenterC61#19417
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #1684

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #21456966C2semidirect
5. #21445275C2semidirect
6. #21445269C2semidirect
7. #21445267C2semidirect
8. #21445223C2semidirect
9. #21445221C2semidirect
10. #21445219C2semidirect
11. #21445217C2semidirect
12. #21444592C2semidirect
13. #21444508C2semidirect
14. #333×D61C2semidirect
15. C61×#1684C2semidirect
279. #1684D61semidirect
345. C61#19417semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#214569662
#214556332
#214556022
#214549292
#214452752
#214452692
#214452672
#214452232
#214452212
#214452192
#214452172
#214445922
#214445082
#333×D612
C61×#16842
#1941761